Vince Cable, Jeremy Hunt, Michael Gove, Ken Clarke and Theresa May are the other ministers who join them when the Inquiry resumes next week.

All eight have applied for core participant status in the Inquiry, which would enable them to obtain advance copies of the written statements of other witnesses, including Andy Coulson and Rebekah Brooks, who will appear before the Inquiry next week.

Lord Justice Leveson is currently ruling on whether to allow the Government as a whole to be given core participant status, or alternatively whether the ministers can individually be given core participant status.

The Government is making a last-minute application to be allowed sight of witness statements submitted by Mr Coulson and Mrs Brooks before they give evidence next week.

If the application is granted by Lord Justice Leveson, the Government will have a right to challenge their evidence and raise objections to potentially sensitive documents being made public by Mr Coulson, David Cameron’s former communications director, and former News International chief executive Mrs Brooks.

Legal experts described the move as “controversial” because Lord Justice Leveson ruled more than a month ago on who would be allowed core participant status in the third module of his Inquiry, which will deal with the relationship between politicians and the press and will begin on Wednesday.

One media lawyer suggested the sudden application had been prompted by “anxiety and nervousness” following damaging disclosures by Rupert and James Murdoch last week about their relationships with ministers, in particular Jeremy Hunt, the Culture Secretary.

David Cameron is likely to face renewed questions about his decision to appoint former News of the World editor Mr Coulson as his communications director when Mr Coulson appears before the Inquiry next Thursday.

Mr Coulson, who resigned last year, is expected to be asked about the process by which he became the Prime Minister’s communications chief, including how thoroughly he was vetted after resigning from the News of the World over the phone-hacking scandal.

The following day Mrs Brooks, who counted the Prime Minister as a personal friend and fellow member of the “Chipping Norton set” in the Cotswolds, is expected to hand over to the Inquiry dozens of private texts and email messages between herself and Mr Cameron.

Both Mr Coulson and Mrs Brooks have been arrested as part of the police investigation into phone-hacking, and both remain on police bail, meaning lawyers for the Leveson Inquiry will not question them about phone-hacking in order to avoid prejudicing any potential trials.

If the Government is successful in its application, which will be heard at 2pm, its lawyers will be entitled to see Mr Coulson and Mrs Brooks’s witness statements and any attached exhibits before they give evidence.

Chris Hutchings, a specialist in media law and partner at Hamlins LLP, said: “This is a controversial move by the Government because the hearing to decide who would be allowed core participant status for the third part of the Inquiry was held more than a month ago.

“The Government chose not to make an application at that stage, and the fact that they are doing so now, so late in the day, suggests they are reacting to events of the past week, and that this has come out of anxiety and nervousness.

“It’s also controversial because it means the Government, which of course commissioned this Inquiry, will be able to challenge the witnesses’ evidence before it is made public, and apply for certain documents to be kept out of the public domain if they object to them.”

Core participant status would also enable lawyers to brief David Cameron and other ministers well in advance of any potential problems that could be raised by Mr Coulson or Mrs Brooks’s evidence.

A spokesman for the Leveson Inquiry confirmed that the Government could have applied for core participant status as long ago as last year, but said it was open for parties to apply at any time.